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• W2105762912 startingPage "3553" @default.
• W2105762912 abstract "We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl–von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers—deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet." @default.
• W2105762912 created "2016-06-24" @default.
• W2105762912 creator A5049172187 @default.
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• W2105762912 date "2012-11-07" @default.
• W2105762912 modified "2023-09-26" @default.
• W2105762912 title "Defects and boundary layers in non-Euclidean plates" @default.
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• W2105762912 doi "https://doi.org/10.1088/0951-7715/25/12/3553" @default.
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